stgsharp/StgSharp.Mathematics/Numeric/MatrixParallel.cs

//-----------------------------------------------------------------------
// -----------------------------------------------------------------------
// file="MatrixParallel"
// Project: StgSharp
// AuthorGroup: Nitload
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using StgSharp.Collections;
using System;
using System.Collections.Generic;
using System.Diagnostics.CodeAnalysis;
using System.Runtime.CompilerServices;
using System.Threading;

namespace StgSharp.Mathematics.Numeric
{
    /*
    * Thread wrapping to accelerate matrix operations by dividing threads into groups (wraps).
    * For M wraps, each containing an average of N threads, we satisfy the condition M * N = T - 4,
    * where T is the total thread count of the CPU. Typically, for modern consumer CPUs, T is around 16.
    * For simplicity, let M * N = 16.
    *
    * The total time complexity for publishing tasks is O(M + N):
    * - O(M) accounts for distributing tasks across M wraps.
    * - O(N) accounts for threads within each wrap fetching tasks from the wrap queue.
    *
    * Using the inequality Sqrt(M * N) <= (M + N) / 2 (derived from the arithmetic-geometric mean inequality),
    * the optimal configuration occurs when M = N. For M * N = 16, this gives M = N = 4.
    * 
    * To ensure compatibility across a wide range of CPU architectures, 
    * we allow each wrap to contain either 3 or 4 threads, providing flexibility while maintaining efficiency.
    */

    public static partial class MatrixParallel
    {

        private static Thread[] _threads;
        private static readonly (int a, int b)[] LookupTable = [
            (1, 1), // 7
            (0, 2), // 8  (no non-zero solution)
            (3, 0), // 9  (no non-zero solution)
            (2, 1), // 10
            (1, 2), // 11
            (0, 3), // 12 (no non-zero solution)
            (3, 1), // 13
            (2, 2), // 14
            (1, 3), // 15
            (4, 1), // 16
            (3, 2), // 17
            (2, 3), // 18
            (1, 4), // 19
            (4, 2), // 20
        ];
        private static bool _meaningful;

        private static volatile int RemainThreadCount = 0;
        private static readonly object _lock = new();
        private static ThreadPriority _AfterWork = ThreadPriority.Lowest;

        public static bool SupportParallel { get; } = Environment.ProcessorCount > 6;

        public static bool IsParallelMeaningful => Environment.ProcessorCount > 6 && IsInitialized;

        public static MatrixParallelWrap.Handle LeaderHandle { get; private/**/ set; }

        private static bool IsInitialized { get; set; } = false;

        private static Queue<IntPtr> LeaderTask { get; set; }

        public static void EndParallel()
        {
            Monitor.Exit(_lock);
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static (int count_3, int count_4) FastDecompose(int c)
        {
            if (c < 7) {
                return (0, 0);
            }

            int t = c - 7;
            int k = t / 14;
            int d = t % 14;

            (int a0, int b0) = LookupTable[d];

            return (a0 + (2 * k), b0 + (2 * k));
        }

        public static void Init()
        {
            if (IsInitialized) {
                return;
            }
            MatrixParallelFactory.Init();
            if (!SupportParallel)
            {
                IsInitialized = true;
                return;
            }
            int count = Environment.ProcessorCount - 4;
            count = count == 5 ? 4 : count;
            _threads = new Thread[count];
            if (count < 6)
            {
                if (count == 3)
                {
                    Wraps = [ new MatrixParallelWrap(0, count, true) ];
                    (LargeWrapCount, SmallWrapCount) = (0, 1);
                    LeaderHandle = new MatrixParallelWrap.Handle(0, Wraps.Peek());
                } else
                {
                    count = 4;
                    Wraps = [ new MatrixParallelWrap(0, count, true) ];
                    (LargeWrapCount, SmallWrapCount) = (1, 0);
                    LeaderHandle = new MatrixParallelWrap.Handle(0, Wraps.Peek());
                }
            } else if (count == 6)
            {
                Wraps = [
                    new MatrixParallelWrap(0, 3, true),
                    new MatrixParallelWrap(3, 3, false)
                ];
                (LargeWrapCount, SmallWrapCount) = (0, 2);
                LeaderHandle = new MatrixParallelWrap.Handle(0, Wraps.Peek());
            } else
            {
                (int _3wrap, int _4wrap) = FastDecompose(count);
                Wraps = new(_4wrap + _3wrap);
                int id = 0, idx = 0;
                for (; idx < _3wrap; idx++, id += 3) {
                    Wraps.Push(new MatrixParallelWrap(idx, 3, id == 0));
                }
                for (; idx < _3wrap + _4wrap; idx++, id += 4) {
                    Wraps.Push(new MatrixParallelWrap(id, 4, id == 0));
                }
                LeaderHandle = new MatrixParallelWrap.Handle(0, Wraps.Peek());
            }
            LeaderTask = LeaderHandle.Wrap.GetWorkerTaskQueue(0);
            IsInitialized = true;
        }

        public static void LaunchParallel(IEnumerable<MatrixParallelWrap> wraps, SleepMode afterWork)
        {
            RemainThreadCount = _threads.Length;
            _AfterWork = (ThreadPriority)afterWork;
            SetAllWrap(wraps);
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static unsafe void MatrixParallelLeaderWork()
        {
            MatrixParallelWrap.ExecuteTaskPackage(LeaderTask);
            _ = Interlocked.Decrement(ref RemainThreadCount);
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static void ResetThreadCount()
        {
            RemainThreadCount = _threads.Length;
        }

        public static void SetAllWrap(IEnumerable<MatrixParallelWrap> wraps)
        {
            ResetThreadCount();
            foreach (MatrixParallelWrap item in wraps) {
                item.SchedulerReset.Set();
            }
        }

        #region wrap field

        private static CapacityFixedStack<MatrixParallelWrap> Wraps;
        private static int LargeWrapCount;
        private static int SmallWrapCount;

        public static CapacityFixedStack<MatrixParallelWrap> LeadParallel()
        {
#if NET9_0_OR_GREATER
#else
            Monitor.Enter(_lock);
#endif

            return Wraps;
        }

        public static void ReleaseParallelLeadership(ref CapacityFixedStack<MatrixParallelWrap> wraps)
        {
#if NET9_0_OR_GREATER
#else
            Monitor.Exit(_lock);
#endif
            wraps = null!;
        }

        #endregion
    }
}